A well-known problem in the art of designing and forming materials into folded networks is that with the exception of deformation at the fold, the material is not significantly stretched, and this imposes simultaneous constraints on the vertices, edges, and facets of a proposed structure and on the process of forming such a structure. However folded structures have many advantages over structures produced by other means such as casting, stamping or assembling, such as cost of manufacture and the versatility to many sheet materials.